Probabilities of Excessive Deviations of Simple Linear Rank Statistics

Abstract

Abstract : Simple linear rank statistics arise in a variety of situations, particularly in the problem of testing the equality of two or more distributions by non-parametric tests. While the asymptotic distributions of simple linear rank statistics have been studied extensively (see, e.g., Hajek and Sidak (1967) ), investigations concerning their large deviation properties have been made only recently (Stone (1967, 1968, 1969) and Woodworth (1970)). In this paper the authors study the rates of convergence to zero of null probabilities of excessive deviations of k-sample (k > or = 2) simple linear rank statistics.